In this chapter we focus on three bio-inspired algorithms and their combinations with fuzzy rule based systems. Rule Based systems are widely being used in decision making, control systems and forecasting. In the real world, much of the knowledge is imprecise and ambiguous but fuzzy logic provides for systems better presentations of the knowledge, which is often expressed in terms of the natura...

This paper introduces a new neurofuzzy model construction and parameter estimation algorithm from observed finite data sets, based on a Takagi and Sugeno (T–S) inference mechanism and a new extended Gram–Schmidt orthogonal decomposition algorithm, for the modeling of a priori unknown dynamical systems in the form of a set of fuzzy rules. The first contribution of the paper is the introduction o...

Fuzzy Newton-Cotes method for integration of fuzzy functions that was proposed by Ahmady in [1]. In this paper we construct error estimate of fuzzy Newton-Cotes method such as fuzzy Trapezoidal rule and fuzzy Simpson rule by using Taylor's series. The corresponding error terms are proven by two theorems. We prove that the fuzzy Trapezoidal rule is accurate for fuzzy polynomial of degree one and...

This paper exploits the ability of Symbiotic Evolution (SE), as a generic methodology, to elicit a fuzzy rule-base of the Mamdani-type. Almost all fuzzy rule-base generation algorithms produce rule-bases with redundant and overlapped membership functions that limit their interpretability elegance in their application. We address this problem by applying an algorithm to merge any similar members...

Systems of fuzzy relation equations are considered as models of fuzzy inference systems. A proper use of an inference mechanism connected to a fuzzy relation modelling a fuzzy rule base is certified by keeping the fundamental interpolation condition. The paper aims at new solutions of systems of fuzzy relation equations and introduces new solvability criteria.

This paper reviews some important points of sparse rule-bases, the reason of their generation and after that three methods are presented, which allow the approximation of the missing rules with reasonable demand on computing. The delimitations and advantages of these methods are presented, too. Fuzzy systems based on a sparse rule-base do not have rules for all the possible combinations of obse...